Working fluid for rankine cycle

ABSTRACT

An organic Rankine cycle working fluid comprising at least one compound having formula (I): RNQ, wherein R is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, N is element nitrogen, the connection of R—N is a ring structure or a straight chain structure, and Q is a hydrogen and/or at least one fluorine atom. A process for converting thermal energy into mechanical energy, a method for power generation, an organic Rankine cycle system, and the use of the working fluid for heat transfer or in a mechanical power generation device are also provided. The organic Rankine cycle working fluid has a high energy conversion efficiency, low flammability, low toxicity and low corrosion on copper.

FIELD OF THE INVENTION

The present invention relates to a working fluid for the organic Rankine cycle, having improved energy conversion efficiency, heat exchange characteristics and thermal stability. The present invention also relates to a process for converting thermal energy to mechanical energy, method for power generation, an organic Rankine cycle system and use of a working fluid for transfer of heat or in a mechanical power generation device.

TECHNICAL BACKGROUND

As energy is becoming an increasingly expensive resource, efforts are made to look for new technologies to generate electricity or useful work from heat sources such as e.g. waste heat from industrial processes and combustion engines, or geothermal heat sources. One way to convert heat energy to mechanical work, useful work, such as electricity is the organic Rankine cycle.

The organic Rankine cycle (ORC) involves an organic fluid with a liquid-vapor phase change occurring at a lower temperature than the water-steam phase change. Due to the organic fluid's low phase change temperature heat recovery from low temperature sources such as industrial waste heat, geothermal heat and solar ponds, is made possible and economical. The low-temperature heat is converted into useful work that can itself be converted into electricity.

In the organic Rankine cycle the working fluid is fed or pumped into a heat exchange relationship with a heat source, e.g. a boiler, where the working fluid is evaporated, thereafter passed through a turbine of some sort and then finally re-condensed.

The ORC could be used for waste heat recovery in e.g. industrial and farming processes, hot exhausts from ovens or furnaces, flue gas condensation, and exhaust gases from vehicles.

The selection of the working fluid is of key importance in low temperature ORCs. Due to the low temperature, heat transfer inefficiencies are highly prejudicial. These inefficiencies depend very strongly on the thermodynamic characteristics of the fluid and on the operating conditions. In order to recover low-grade heat, the fluid generally has a lower boiling temperature than water. Refrigerants and hydrocarbons are the two commonly used components. Most researchers choose existing refrigerants, such as R152a or R134a, as working fluids of the ORC.

A general disadvantage of most working fluids made commercial for organic Rankine cycles are the fact that they have been designed specifically for the refrigeration cycle commonly used in air condition systems and heat pump systems. However, the refrigeration cycle is the anti-cycle of the Carnot cycle to generate power. Thus, working fluids for the purpose to generate power from low-grade heat should have distinct features from refrigerants. A pressure-enthalpy graph is shown in FIG. 1. The energy conversion process is from point H3 to point H4. For refrigeration applications, the working fluid should influence to decrease the enthalpy difference between H3 and H4 in order to reduce the compressor power. For the ORC, the working fluid should influence to increase the enthalpy difference between H3 and H4 in order to convert more power from heat.

Some refrigerants like e.g. R600a, are also used as working fluids in the ORC to convert heat to electrical power but the flammability of the R600a is a big problem inmost industrial or commercial environments. Isobutane used as a refrigerant in domestic refrigerators may upon leakage into the refrigerator cabinet be ignited by sparks from the electrical system. The use of a flammable gas as a refrigerant is quite dangerous and encompasses a great deal of risk. The normal risks that chlorofluorocarbon compounds (CFC) or other potentially toxic refrigerants would have upon escape, are mainly related to depletion of breathable air and frosting at the point of escape.

The ozone depletion potential (ODP) of a chemical compound is the relative amount of degradation of the ozone layer it may cause. ODP of a specific substance is defined as the ratio of global loss of ozone due to given substance over the global loss of ozone due the same mass of trichlorofluoro-methane (R-11 or CFC-11) having a fixed ODP of 1.0. R11 has the maximum potential amongst all chlorocarbons due to the presence of three chlorine atoms in the molecule. Chlorodifluoromethane (R-22) has an ODP of 0.05. Thus, the ODP can be estimated from the structure of a given substance. Chlorofluorocarbons have ODPs in the vicinity of 1 and hydrochlorofluoro-carbons (HCFC) have ODPs often in the range of 0.005 to 0.2, since the presence of hydrogen causes the compounds to react readily in the troposphere, therefore reducing their chance to reach the stratosphere. Hydrofluorocarbons (HFC) have no chlorine content, so their ODPs are essentially zero. Some used refrigerants such as CFCs, HCFCs and HFCs, e.g. R11 and R22, show relatively good performance on heat efficiency in the ORC but due to stricter environmental legislations such refrigerants, due to their halogen content, already have been or in the near future probably will be phased out from the market.

Other features affecting the choice of a chemical in an ORC may be the resistance to corrosion on copper and the global warming potential (GWP).

US 2010/139274 discloses chloro- and bromo-fluoro-olefins useful as organic Rankine cycle working fluids for efficiently converting waste heat generated from industrial processes, such as electric power generation from fuel cells, into mechanical energy or further to electric power.

WO 2006/014609 discloses a process for recovering heat and a working fluid for an organic Rankine cycle system comprising one or more compounds of Formula (I) (I) CR′y, wherein y is 3 or 4 and each R′ is independently H, F, I, Br, substituted or unsubstituted C3-C9 alkyl, substituted or unsubstituted C2-C9 alkoxy, substituted or unsubstituted fluoropolyether, substituted or unsubstituted C2-C9 alkenyl, substituted or unsubstituted aryl, substituted or unsubstituted C6-C9 alkylaryl, or substituted or unsubstituted C6-C9 alkenyaryl, provided said compound includes at least two carbon atoms, at least one fluorine atom, and no chloride atoms, and further provided that any OH substituted alkyl preferably has at least three carbon atoms.

U.S. Pat. No. 4,541,943 discloses a working fluid to be used in a mechanical vapor recompression heat pump system. The working fluid can be either a saturated hydrocarbon or a fluorohydrocarbon ether or a fluorinated amine. Also, the heat pumps may operate on reverse Rankine cycle.

US 2010/0095703 discloses a working medium for refrigeration processes comprising at least one sorbent material and at least one refrigerant. The sorbent material contains at least one nonvolatile organic salt. A list of suitable anions to be included in the salt is presented. The list of anions includes bis(perfluoroalkylsulfonyl)amides. Suitable ionic liquids are 1-methyl-3-octylimidazolium tetrafluoroborate and butylmethylpyrrolidinium bis(trifluoromethylsulfonyl)-imide.

As disclosed above legislations are pushing towards more reuse of heat thus making an incentive to reuse low grade heat not normally considered economical to do. In the future a choice between high fines for releasing waste heat into the environment and reusing the generated waste heat to a large extent is probable. In view of this the choice of working media becomes crucial. There exists a need to find new working fluids for use in an ORC to achieve a high output of work from the retrieved heat in a resource effective and thus economically favourable way.

SUMMARY OF THE INVENTION

It is an object of this invention to provide working fluids for an organic Rankine cycle which fluids can increase the efficiency of conversion of thermal energy to mechanical energy.

It is another object of this invention to provide working fluids for a organic Rankine cycle which fluids are stable and can be used safely.

The characteristics for the working fluid according to the present invention is a high thermal efficiency, low or reasonable flammability, low or reasonable toxicity (i.e. low degree of poisoning during operation, no or low ODP and low or reasonable corrosion on copper (if this material is used for e.g. pipings and/or heat exchanger).

The working fluids according to the present invention comprise at least one compound having a structure according to Formula (I):

RNQ

wherein R is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl, N is the element nitrogen, the connection of R—N is a ring structure (i.e. a heterogeneous ring) or a straight chain structure, and Q is chosen from a hydrogen atom and/or at least one fluorine atom.

One embodiment of the present invention relates to an organic Rankine cycle working fluid comprising at least one compound having either the Formula (II):

R¹NH_(n)F_(2-n),

wherein R¹ is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and n is 0 or 1; or

the Formula (III):

wherein R² and R³ are independently chosen from H₂, F₂ and HF, and p is 0 or 1, preferably 1.

Preferably, R¹ in Formula (II) is a fluorinated or non-fluorinated methyl or ethyl group.

Preferably, said compound according to Formula (II) is chosen from the group consisting of CH₃NHF, CH₂FNHF, CHF₂NHF, CF₃NHF, CH₃NF₂, CH₂FNF₂, CHF₂NF₂, CF₃NF₂, C₂H₅NHF, CH₂FCH₂NHF, CHF₂CH₂NHF, CH₃CHFNHF, CH₂FCHFNHF, C₂H₅NF₂, CH₂FCH₂NF₂, CH₃CHFNF₂, and CHF₂CF₂NF₂; preferably CH₃NF₂, CH₂FNF₂, CHF₂NF₂, and CF₃NF₂.

R² in Formula (III) contains preferably at least one fluorine. The compound according to Formula (III) is preferably tetrafluoroaziridine.

In another embodiment of the present invention relates to a process for converting thermal energy to mechanical energy in an organic Rankine cycle comprising the steps of:

a) vaporizing a liquid working fluid according to the present invention, by bringing it in contact with a heat source; b) expanding the vaporized working fluid, wherein said heat is converted into mechanical work; and c) cooling the expanded vaporized working fluid with a cooling source to condense the vapor to liquid phase.

In an embodiment the temperature of the working fluid after being brought in contact with a heat source in a) is at most 100° C., preferably said temperature is 25 to 90° C.

Another embodiment of the present invention relates to an organic Rankine cycle system using the working fluid according to the present invention for a heat cycle.

Still another embodiment of the present invention relates to an organic Rankine cycle system comprising:

(a) a working fluid according to the present invention; (b) a heat exchanging device containing said working fluid, connected to a heat source, for vaporizing the working fluid; (c) an expansion device responsive to said vaporized working fluid for expanding said working fluid vapor resulting in heat depleted working fluid; (d) an electric generator driven by said expansion device for producing electrical power; (e) a condenser for condensing the heat depleted working fluid and producing condensate; and (f) means for effecting the return of said condensate to said heat exchanging device.

In one embodiment of the present invention the heat source is heat from a boiler or a fuel cell, waste heat from an industrial or farming process, geothermal heat, waste heat from a combustion engine or power plant, or solar heat.

In a further embodiment the expander is a turbine, screw expander, scroll expander, or piston expander.

Still one embodiment relates to use of a working fluid according to the present invention for transfer of heat.

Yet another embodiment relates to use of a working fluid according the present invention in a mechanical power generation device adapted to use an organic Rankine cycle or a modification thereof.

Another embodiment relates to a method for power generation comprising transfer of heat using a working fluid according to the present invention.

One embodiment relates to a method for power generation according to the present invention, using a Rankine cycle or a modification thereof to generate work from heat.

Another embodiment relates to a compound having the Formula (IV):

SHORT SUMMARY OF THE DRAWINGS

FIG. 1 shows a pressure-enthalpy graph.

FIG. 2 shows a graph of the entropy and efficiency for known existing working fluids of the ORC for a temperature shift between 20 to 60° C. in the system. This temperature cycle in the ORC, i.e. 60° C. is the evaporating temperature for the working fluid and 20° C. is the condensing temperature, is in the following referred to as an ORC 20-60 cycle.

FIG. 3 shows a schematic drawing of an organic Rankine Cycle system.

DETAILED DESCRIPTION OF THE INVENTION

Conversion of low grade heat into work and thereafter to electricity using the highest efficiency is in many cases obtained by using an ORC. A heat source supplies heat to an ORC with the aid of a heat exchanging device. The temperature of the working fluid in the ORC in this heat exchanging section can be below 90° C. Thus, heat sources suitable for use in the ORC include industrial waste heat or geothermal waste heat. One advantage of the working fluid according to the present invention is that it increases the thermal efficiency in the conversion of heat into work. The heat source is able to give the working fluid in the ORC system a temperature of at most 100° C., preferably at most 90° C., preferably at most 80° C., and at least a temperature of 25° C., preferably 30-75° C., e.g. 40-70° C., 40-65° C., or 50-70° C., in the heat retrieving section (the evaporation section) of the ORC.

By investigating the relation between the entropy and efficiency of ORC for corresponding working fluids, it has been found that, generally speaking, working fluids with low absolute entropy (i.e. the entropy at OK, (−273° C.)) will have higher efficiencies. This result is shown in FIG. 2 in which the ORC at 20° C.-60° C. is taken as an example. The third law of thermodynamics relates itself to the entropy of a system. It states that the entropy of a pure substance approaches zero as the temperature approaches absolute zero. This law provides a reference point in the calculation of the entropy, where the entropy calculated relative to this point is considered the absolute entropy. Here, the thermodynamic property (absolute entropy) in the gaseous state at the 293.15K, 101.325 KPa is calculated for all the molecules using density functional theory (DFT) with Gaussian 09 program. Absolute entropy means the increment of entropy when the temperature is increased from OK to 293.15K. All calculations for the molecules were carried out with B3LYP/6-31 G(d) Opt Freq. The calculation results of absolute entropy are in good agreement with experimental data, although only a few such data are available. On the calculation results of absolute entropy, the calculation results obtained by B3LYP/6-31G(d) seem to be accurate, since Gaussian employ the mature theoretical methods and statistical thermodynamics to compute this thermodynamic properties, and this computational level is moderate.

All the data of the working fluids to calculate the efficiencies n, are taken from the software Refprop8.0. The values of entropy are calculated from software Gaussian 03 by the HF/3-21 G method. Presenting a working fluid having molecules with low entropies has been found of interest according to the present invention.

Thus, it has been found that the working fluids according to the present invention are to be selected from molecule structures which might contribute to less entropy, such as cyclic structures, double bonds, triple bonds, and/or molecules with a low total number of atoms but with proper boiling point. Also, atoms making up the working fluid according to the present invention are four atoms, i.e. C, N, F and H.

Workings fluids used in an ORC preferably present characteristics like:

-   -   a) an isentropic saturation vapor curve, and preferably         displaying a small superheating at the exhaust of the         evaporator;     -   b) a low freezing point and high stability temperature, wherein         the freezing point should be lower than the lowest temperature         in the cycle and maximum temperature of the heat source is         limited by the chemical stability of the working fluid;     -   c) a high heat of vaporization and density, since a fluid with a         high latent heat and density will absorb more energy from the         heat source in the evaporator;     -   d) a low environmental impact, wherein the ozone depletion         potential (ODP) and the global warming potential (GWP) are         examples of such parameters; and     -   e) low flammability, and low or no toxicity.

It has been found that the working fluids according to the present invention present a high efficiency in an ORC compared to conventional working fluids.

A working fluid according to the present invention comprises at least one compound having a structure according to Formula (I):

RNQ

wherein R is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl, N is the element nitrogen, the connection of R—N is a ring structure (i.e. a heterogeneous ring) or a straight chain structure, and Q is chosen from a hydrogen atom and/or at least one fluorine atom.

Preferably the working fluid according to the present invention comprises at least one compound having either the Formula (II):

R¹NH_(n)F_(2-n),

wherein R¹ is fluorinated or non-fluorinated methyl, ethyl, vinyl or ethynyl, and n is 0 or 1; or

the Formula (III):

wherein R² and R³ are independently chosen from H₂, F₂ and HF, and p is 0 or 1.

If the working fluid comprises a compound having a structure according to Formula (II) R¹ may be non-fluorinated, or fully or partially fluorinated. In one preferred embodiment R¹ is a fluorinated or non-fluorinated methyl or ethyl group. Preferred compounds according to Formula (II) are chosen from CH₃NHF, CH₂FNHF, CHF₂NHF, CF₃NHF, CH₃NF₂, CH₂FNF₂, CHF₂NF₂, CF₃NF₂, C₂H₅NHF, CH₂FCH₂NHF, CHF₂CH₂NHF, CH₃CHFNHF, CH₂FCHFNHF, C₂H₅NF₂, CH₂FCH₂NF₂, CH₃CHFNF₂, CHF₂CF₂NF₂, in particular CH₃NHF, CH₂FNHF, CHF₂NHF, CF₃NHF, CH₃NF₂, CH₂FNF₂, CHF₂NF₂, CF₃NF₂, C₂H₅NHF, CH₂FCH₂NHF, CHF₂CH₂NHF, CH₃CHFNHF, and CH₂FCHFNHF.

More preferably R¹ is a fluorinated or non-fluorinated methyl group, and especially in combination with p being 0.

If the working fluid comprises a compound having a structure according to Formula (III) it is preferred that p is 1. Regarding R² and R³, the more fluorine that is present in Formula (III) the better the compound seems to perform in an ORC. Thus, fluorinated aziridines are preferred.

When comparing which compounds of the Formula (I) are preferred according to the present invention, it has been found that compounds having either Formula (II) or Formula (III) are preferable. However, comparing the compounds having either Formula (II) or Formula (III), compounds according to Formula (II) are considered preferable. In turn, of the compounds according to Formula (II) the ones having only one carbon atom are preferred according to the present invention.

The compound according to Formula (I), such as e.g. Formula (II) and/or (III), preferably constitutes the main part of the working fluid. Preferably the compound according to Formula (I), such as e.g. Formula (II) and/or (III), constitutes 60-100%, by weight of the working fluid, preferably 80-100%, more preferably 90-100%, most preferably 95-100%, by weight.

One of the more preferred compounds having Formula (III) is tetrafluoroaziridine. The synthesis of the tetrafluoroaziridin may be done by the following reaction steps:

Tetrafluoroethene and triethylammoniumazide react in sym-tetrachloro-ethane at −5° C. to generate intermediates with one negative charge. The unstable intermediates decompose immediately to produce tetrafluorovinylazide. The tetrafluorovinylazide decomposes at a convenient rate at a temperature of 25 to 40° C. and lose nitrogen to form 2,3,3-trifluoro-2H-aziridine. 2,3,3-trifluoro-2H-aziridine reacts with hydrogen fluoride at a temperature of 25° C. to produce tetrafluoroaziridine.

Calculations

Disclosed below are the calculations which have been used as basis for determining which molecule structures have an increased efficiency in the ORC. The compounds for use in a working fluid according to the present invention were chosen on the basis of these calculations. By using a working fluid with an increased efficiency in the ORC more of the transferred heat may be made into work. Also, by using a working fluid having an increased efficiency heating sources of lower temperatures can become economical to recover heat from and make into work.

Group Contribution Method

The performed calculations for efficiency have been compensated in view of the contribution that different chemical groups make. The group contribution method has been made to get a more accurate value in practice. Disclosed below is a calculation on one example to show how to calculate the data based on the chemical structure. All compounds according to the present invention with the disclosed specific molecule structures have been calculated with this method by computer.

Sample Molecule

CF₃NF₂ molecule weight: M=121.01

-   -   Calculating the normal boiling point T_(b) by Joback method

Number of Group groups ΔT_(bi)

1 18.25

1 11.74 —F 5    −0.03 × 5 Total 29.84

$\begin{matrix} {T_{b} = {198 + {\Sigma \; n_{i}\Delta \; T_{bi}}}} \\ {= {198 + 29.84}} \\ {= {227.84\mspace{14mu} K}} \end{matrix}$

-   -   Calculating the latent heat ΔH_(v) at 60° C. by CSGC-HW1 method

Number of Group groups ΔT_(i) ΔP_(i)

1 0.002200289 −0.003474154

1 −0.009525362   −0.07779588   —F 5     0.014653116 × 5      0.108614823 × 5 Total 0.065940508 0.46184082

$\begin{matrix} {T_{c}^{*} = {T_{b}/\left\lbrack {A_{T} + {B_{T}\Sigma \; n_{i}\Delta \; T_{i}} + {C_{T}\left( {\Sigma \; n_{i}\Delta \; T_{i}} \right)}^{2} + {D_{T}\left( {\Sigma \; n_{i}\Delta \; T_{i}} \right)}^{3}} \right\rbrack}} \\ {= {227.84/\left\lbrack {0.5782359 + {1.064102 \times 0.065940508} - {1.780121 \times}} \right.}} \\ \left. {0.065940508^{2} - {0.5002329 \times 0.065940508^{3}}} \right\rbrack \\ {= {355.65\mspace{14mu} K}} \end{matrix}$ $\begin{matrix} {P_{c}^{*} = {1.01325\; \ln \; {T_{b}/\left\lbrack {A_{P} + {B_{P}\Sigma \; n_{i}\Delta \; P_{i}} + {C_{P}\left( {\Sigma \; n_{i}\Delta \; P_{i}} \right)}^{2} + {D_{P}\left( {\Sigma \; n_{i}\Delta \; P_{i}} \right)}^{3}} \right\rbrack}}} \\ {= {1.01325\mspace{14mu} \ln \mspace{14mu} {227.84/\left\lbrack {0.029125 + {0.207087 \times 0.46184082} -} \right.}}} \\ \left. {{0.04948187 \times 0.46184082^{2}} - {0.08637077 \times 0.46184082^{3}}} \right\rbrack \\ {= {52.04\mspace{14mu} {bar}}} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {T_{br}^{*} = {T_{b}/T_{c}^{*}}}} \\ {= {227.84/355.65}} \\ {= 0.6405} \end{matrix}$ $\begin{matrix} {{\Delta \; H_{vb}} = {1.319767\; R\mspace{14mu} T_{c}^{*}{{T_{br}^{*}\left\lbrack {{\ln \left( {P_{c}^{*}/1.01325} \right)} - 1.140257} \right\rbrack}/\left( {1.059397 - T_{br}^{*}} \right)}}} \\ {= {1.319767 \times 8.314 \times 355.65 \times 0.6405 \times \left\lbrack {{\ln \left( {52.04/1.01325} \right)} -} \right.}} \\ {\left. 1.140257 \right\rbrack/\left( {1.059397 - 0.6405} \right)} \\ {= {18031.90\mspace{14mu} J\text{/}{mol}}} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {q = {{0.7815677\mspace{14mu} T_{br}^{*}} - 0.1072383}}} \\ {= {{0.7815677 \times 0.6405} - 0.1072383}} \\ {= 0.3934} \end{matrix}$ $\mspace{79mu} \begin{matrix} {T_{r}^{*} = {T/T_{c}^{*}}} \\ {= {\left( {60 + 273.15} \right)/355.65}} \\ {= 0.9366} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {{\Delta \; H_{v}} = {\Delta \; {H_{vb}\left\lbrack {\left( {1 - T_{r}^{*}} \right)/\left( {1 - T_{br}^{*}} \right)} \right\rbrack}^{q}}}} \\ {= {18048.07 \times \left\lbrack {\left( {1 - 0.9366} \right)/\left( {1 - 0.6405} \right)} \right\rbrack^{0.3934}}} \\ {= {9113.21\mspace{14mu} J\text{/}{mol}}} \end{matrix}$

-   -   Calculating saturated vapor pressure at 60° C. by CSGC-PR method

Number of Group groups ΔT_(i) × 10⁴ ΔP_(i) × 10³

1  27.54   −2.68

1 338.14 123.74 —F 5  35.32 × 5  12.25 × 5 Total  0.054228  0.18213

$\begin{matrix} {T_{c}^{*} = {T_{b}/\left\lbrack {A_{T} + {B_{T}\Sigma \; n_{i}\Delta \; T_{i}} + {C_{T}\left( {\Sigma \; n_{i}\Delta \; T_{i}} \right)}^{2} + {D_{T}\left( {\Sigma \; n_{i}\Delta \; T_{i}} \right)}^{3}} \right\rbrack}} \\ {= {227.84/\left\lbrack {0.5782585 + {1.061273 \times 0.054228} - {1.778714 \times}} \right.}} \\ {{0.054228^{2} - {0.4998375 \times 0.054228^{3}}}} \\ {= {361.36\mspace{14mu} K}} \end{matrix}$ $\begin{matrix} {P_{c}^{*} = {1.01325\mspace{14mu} \ln \mspace{14mu} {T_{b}/\left\lbrack {A_{P} + {B_{P}\Sigma \; n_{i}\Delta \; P_{i}} + {C_{P}\left( {\Sigma \; n_{i}\Delta \; P_{i}} \right)}^{2} + {D_{P}\left( {\Sigma \; n_{i}\Delta \; P_{i}} \right)}^{3}} \right\rbrack}}} \\ {= {1.01325\mspace{14mu} \ln \mspace{14mu} {227.84/\left\lbrack {0.04564342 + {0.3046466 \times 0.18213} -} \right.}}} \\ \left. {{0.0652039 \times 0.18213^{2}} - {0.04390779 \times 0.18213^{3}}} \right\rbrack \\ {= {55.73\mspace{14mu} {bar}}} \end{matrix}$ $\mspace{79mu} \begin{matrix} {T_{r}^{*} = {T/T_{c}^{*}}} \\ {= {\left( {60 + 273.125} \right)/361.36}} \\ {= 0.9216} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {T_{br}^{*} = {T_{b}/T_{c}^{*}}}} \\ {= {227.84/361.36}} \\ {= 0.6305} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {\phi_{b} = {{- 35} + {36/T_{br}^{*}} + {42\mspace{14mu} \ln \mspace{14mu} T_{br}^{*}} - T_{br}^{*6}}}} \\ {= {{- 35} + {36/0.6305} + {42\mspace{14mu} \ln \mspace{14mu} 0.6305} - 0.6305^{6}}} \\ {= 2.663} \end{matrix}$ $\begin{matrix} {\alpha_{c} = {\left\lbrack {{0.315\phi_{b}} + {\ln \left( {P_{c}^{*}/1.01325} \right)}} \right\rbrack/\left( {{0.0838\phi_{b}} - {\ln \mspace{14mu} T_{br}^{*}}} \right)}} \\ {= {\left\lbrack {{0.315 \times 2.663} + \mspace{14mu} {\ln \left( {55.73/1.01325} \right)}} \right\rbrack/\left( {{0.0838 \times 2.663} - {\ln \mspace{14mu} 0.6305}} \right)}} \\ {= 7.0811} \end{matrix}$ $\mspace{20mu} \begin{matrix} {Q = {0.0838\left( {3.758 - \alpha_{c}} \right)}} \\ {= {0.0838 \times \left( {3.758 - 7.0811} \right)}} \\ {= {- 0.2785}} \end{matrix}$ $\mspace{20mu} \begin{matrix} {A = {{- 35}\; Q}} \\ {= {{- 35} \times \left( {- 0.2785} \right)}} \\ {= 9.747} \end{matrix}$ $\mspace{20mu} \begin{matrix} {B = {{- 36}\; Q}} \\ {= {{- 36} \times \left( {- 0.2785} \right)}} \\ {= 10.025} \end{matrix}$ $\mspace{20mu} \begin{matrix} {C = {{{- 42}\; Q} + \alpha_{c}}} \\ {= {{42 \times \left( {- 0.2785} \right)} + 7.0811}} \\ {= {- 4.615}} \end{matrix}$ $\mspace{20mu} \begin{matrix} {D = {- Q}} \\ {= 0.2785} \end{matrix}$ $\begin{matrix} {{\ln \mspace{14mu} P_{r}^{*}} = {A - {B/T_{r}^{*}} + {C\; \ln \mspace{14mu} T_{r}^{*}} + {D\mspace{14mu} T_{r}^{*6}}}} \\ {= {9.747 - {10.025/0.9216} - {4.850 \times \ln \mspace{14mu} 0.9216} + {0.2683 \times 0.9216^{6}}}} \\ {= {- 0.5814}} \end{matrix}$

Because P_(r)*=P_(60° C.)/P_(c)*

we have P_(60° C.)=P_(c)*P_(r)*=55.73×exp(−0.5814)=31.161 bar. Through the similar procedure, we can obtain the saturated vapor pressure at 20° C.:

P_(20° C.)=11.595 bar

-   -   Calculating the corresponding specific volume of the saturated         vapor at 60° C.         First, the T₀ and P_(c) were calculated using Joback method:

Number of Group groups ΔT_(ci) ΔP_(ci)

1 0.067 −0.0168

1 0.0169   0.0074 —F 5 0.0111 × 5 −0.0057 × 5 Total 0.0791 −0.0168

$\begin{matrix} {T_{c} = {T_{b}/\left\lbrack {0.584 + {0.965\Sigma \; n_{i}\Delta \; T} - \left( {\Sigma \; n_{i}\Delta \; T_{i}} \right)^{2}} \right\rbrack}} \\ {= {227.84/\left\lbrack {0.584 + {0.965 \times 0.0791} - 0.0791^{2}} \right\rbrack}} \\ {= {348.3\mspace{14mu} K}} \end{matrix}$ $\begin{matrix} {P_{c} = \left( {0.113 + {0.0032\; n_{A}} - {\Sigma \; n_{i}\Delta \; P_{i}}} \right)^{- 2}} \\ {= \left( {0.113 + {0.0032 \times 7} - 0.0168} \right)^{- 2}} \\ {= {43.17\mspace{14mu} {bar}}} \end{matrix}$

Secondly, we calculate the saturated vapor pressure at T_(r)=0.7 (T=T_(r)*T_(c)=0.7×348.3=243.8 K) by the CSGC-PR method mentioned above, and the result is:

P_(ω) = 2.12  bar $\begin{matrix} {\omega = {{- {lgP}_{\omega \; r}} - 1.0}} \\ {= {{\lg \left( {P_{\omega}/P_{c}} \right)} - 1.0}} \\ {= {{- {\lg \left( {2.12/43.17} \right)}} - 1.0}} \\ {= 0.309} \end{matrix}$ $\begin{matrix} {T_{r} = {T/T_{c}}} \\ {= {333.15/348.3}} \\ {= 0.9565} \end{matrix}$ $\begin{matrix} {P_{r} = {P_{60{^\circ}\mspace{14mu} {C.}}/P_{c}}} \\ {= {31.161/43.17}} \\ {= 0.7218} \end{matrix}$ $\begin{matrix} {B^{(0)} = {0.083 - {0.422/T_{r}^{1.6}}}} \\ {= {0.0083 - {0.4220/0.9565^{1.6}}}} \\ {= {- 0.37012}} \end{matrix}$ $\begin{matrix} {B^{(1)} = {0.139 - {0.172/T_{r}^{4.2}}}} \\ {= {0.139 - {0.172/0.9565^{4.2}}}} \\ {= {- 0.0683}} \end{matrix}$ PV = ZRT PV = [1 + (B⁽⁰⁾ + ω B⁽¹⁾)T_(r)/P_(r)]RT $\begin{matrix} {V = {\left( {{T_{r}/P_{r}} + B^{(0)} + {\omega \; B^{(1)}}} \right){{RT}_{c}/P_{c}}}} \\ {= {\left\lbrack {{0.9565/0.7218} - 0.37012 + {0.309 \times \left( {- 0.0683} \right)}} \right\rbrack \times}} \\ {{8.3145 \times {{348.3/43.17}/100}}} \\ {= {0.62656\mspace{14mu} L\text{/}{mol}}} \end{matrix}$ $\begin{matrix} {V_{g\mspace{14mu} 60{^\circ}\mspace{14mu} {C.}} = {V/M}} \\ {= {0.62656/121.01}} \\ {= {0.00518\mspace{14mu} m^{3}\text{/}{Kg}}} \end{matrix}$ $\begin{matrix} {{PV} = P_{60{^\circ}\mspace{14mu} {C.V_{g\mspace{14mu} 60{^\circ}\mspace{14mu} C}}}} \\ {= {31.161 \times 0.00518 \times 1000}} \\ {= {16.31\mspace{14mu} {Kj}\text{/}{Kg}}} \end{matrix}$

Similarly, we can also figure out the specific volume of the vapor at 20° C.:

V_(g  20^(∘)  C.) = 0.01438  m³/Kg $\begin{matrix} {{V_{4}/V_{3}} = {V_{g\mspace{14mu} 20{^\circ}\mspace{14mu} {C.}}/V_{g\mspace{14mu} 60{^\circ}\mspace{14mu} {C.}}}} \\ {= {0.01438/0.00518}} \\ {= 2.69} \end{matrix}$

-   -   Calculating the corresponding specific heat of the saturated         liquid at 40° C. The Rozicka-Domalski method was used to         calculate the C_(pl) at 40° C.

Number of Group groups a_(i) B_(i) c_(i) —CF₃ 1 15.423 −9.2464 2.8647 —NF₂ 1 6.1358 −0.17365 0.026272 Total 21.5588 −9.42005 2.890972

$\begin{matrix} {T = {40 + 273.15}} \\ {= {313.15\mspace{14mu} K}} \end{matrix}$ C_(pl)/R = Σ n_(i)a_(i) + Σ n_(i)b_(i)(T/100) + Σ n_(i)c_(i)(T/100)² $\begin{matrix} {C_{pl} = {R \times \left\{ {{\Sigma \; n_{i}a_{i}} + {\Sigma \; n_{i}{b_{i}\left( {T/100} \right)}} + {\Sigma \; n_{i}{c_{i}\left( {T/100} \right)}^{2}}} \right\}}} \\ {= {8.3145 \times \left\{ {21.5588 + {\left( {- 9.42005} \right) \times \left( {313.15/100} \right)} +} \right.}} \\ \left. {2.890972 \times \left( {313.15/100} \right)^{2}} \right\} \\ {= {169.695\mspace{14mu} J\text{/}{{mol} \cdot K}}} \\ {= {1.402\mspace{14mu} {Kj}\text{/}{{Kg} \cdot K}}} \end{matrix}$

-   -   Calculating the thermal efficiency of the ORC 20-60 cycle:

$\begin{matrix} {\eta_{GC} = \frac{P_{1}V\mspace{14mu} \ln \mspace{14mu} \frac{P_{1}}{P_{2}}}{{VH}_{v} + {C_{p\; 1}\left( {T_{1} - T_{2}} \right)}}} \\ {= {16.31 \times {{\ln \left( {31.161/11.595} \right)}/\left\lbrack {75.31 + {1.402 \times \left( {60 - 20} \right)}} \right\rbrack}}} \\ {= {12.14\%}} \end{matrix}$

Since the thermal efficiency correction scale factor is −0.652% So the final result is η=12.14%-0.652%=11.49% In conclusion:

At 60° C.:

ΔH_(v)=9113.21 J/mol=75.31 kJ/kg

P_(60° C.)=31.161 bar

v_(g 60° C.)=0.00518 m³/Kg PV=16.31 kJ/kg

At 20° C.: P_(20° C.)=11.595 bar

v_(g 20° C.)=0.01438 m³/Kg v₄/v₃=2.69

At 40° C.: C_(pl)=1.402 Kj/Kg·K

η=11.49% The same types of calculations are made for all molecules according to the present invention.

TABLE 1 Results from group contribution calculations Latent Critical heat Specific points P1 P2 v_(g3) v₄ v_(g4) Density_(4l) v_(l) ΔH_(v) heat C_(p) PV Molecules (K) MPa MPa m³/Kg m³/Kg m³/Kg Kg/m³ m³/Kg (kJ/kg) (kJ/kg•K) kJ/kg CH3—NHF 428.8 0.7866 0.2323 0.0633 0.2143 0.2023 693.552 0.00144 411.46 2.208 49.78 CH2F—NHF 418.8 0.8415 0.2437 0.0428 0.14778 0.1404 772.906 0.00129 299.72 1.827 36.01 CHF2—NHF 412.4 0.8863 0.2567 0.0317 0.10958 0.1047 854.775 0.00117 232.59 1.571 28.13 CF3—NHF 406.3 0.9737 0.2914 0.0235 0.07857 0.0755 1,025.16 0.00098 182.95 1.38 22.9 CH3—NF2 406.6 1.1723 0.3875 0.0297 0.08977 0.0863 923.882 0.00108 255.15 1.721 34.79 CH2F—NF2 360 2.698 0.9858 0.0089 0.02445 0.0248 1,028.57 0.00097 134.02 1.664 24.1 CHF2—NF2 354.4 2.859 1.0426 0.0068 0.01868 0.0191 1,108.33 0.0009 102.21 1.513 19.47 CF3—NF2 348.4 3.1125 1.1585 0.0052 0.01393 0.0144 1,271.63 0.00079 75.27 1.402 16.13 CH3—CH2—NHF 453.5 0.3772 0.0957 0.1069 0.4215 0.3906 672.635 0.00149 378.33 2.154 40.34 CH2F—CH2—NHF 443.7 0.398 0.0984 0.0783 0.37989 0.295 669.078 0.00149 295.97 1.849 37.38 CHF2—CH2—NHF 437.5 0.418 0.1032 0.0607 0.28125 0.2296 704.21 0.00142 240.21 1.622 29.02 CF3—CH2—NHF 431.6 0.4641 0.119 0.0458 0.19913 0.1676 833.068 0.0012 195.41 1.442 23.7 CH3—CHF—NHF 446.9 0.396 0.1002 0.0788 0.19909 0.2896 760.097 0.00132 292.16 1.808 19.95 CH2F—CHF—NHF 437.5 0.418 0.1032 0.0607 0.28116 0.2296 704.21 0.00142 240.21 1.622 29.02 CHF2—CHF—NHF 431.5 0.4393 0.1083 0.0485 0.21881 0.1847 714.374 0.0014 201.48 1.466 23.7 CF3—CHF—NHF 425.6 0.4879 0.1249 0.0375 0.16016 0.1381 826.802 0.00121 167.69 1.33 20 CH3—CF2—NHF 440.8 0.4388 0.1152 0.0576 0.14968 0.2051 922.119 0.00108 230.17 1.561 17.24 CH2F—CF2—NHF 431.6 0.4641 0.119 0.0458 0.19857 0.1676 833.068 0.0012 195.41 1.442 23.63 CHF2—CF2—NHF 425.6 0.4879 0.1249 0.0375 0.15972 0.1381 826.791 0.00121 167.7 1.33 19.95 CF3—CF2—NHF 419.8 0.5407 0.1435 0.0295 0.52019 0.1054 939.588 0.00106 141.91 1.228 74.65 CH3—CH2—NF2 395 1.2373 0.4077 0.0228 0.06906 0.0671 921.083 0.00109 203.1 1.79 28.16 CH2F—CH2—NF2 386.3 1.3348 0.4322 0.017 0.06328 0.0514 903.794 0.00111 162.58 1.616 27.35 CHF2—CH2—NF2 380.6 1.411 0.4565 0.0134 0.04867 0.0409 927.941 0.00108 133.52 1.469 22.22 CF3—CH2—NF2 374.8 1.5417 0.5128 0.0104 0.03641 0.0312 1,064.63 0.00094 108.11 1.345 18.67 CH3—CHF—NF2 389.1 1.3039 0.4297 0.0174 0.03721 0.0518 1,012.68 0.00099 161.79 1.579 15.99 CH2F—CHF—NF2 380.6 1.411 0.4565 0.0134 0.04872 0.0409 927.941 0.00108 133.52 1.469 22.24 CHF2—CHF—NF2 375.3 1.4895 0.4817 0.0108 0.03876 0.0334 929.472 0.00108 111.69 1.362 18.67 CF3—CHF—NF2 369.4 1.6326 0.542 0.0085 0.02964 0.0258 1,042.93 0.00096 91.63 1.269 16.07 CH3—CF2—NF2 383.1 1.4215 0.4817 0.0133 0.02906 0.0386 1,177.56 0.00085 128.9 1.416 14 CH2F—CF2—NF2 374.8 1.5417 0.5128 0.0104 0.0363 0.0312 1,064.63 0.00094 108.11 1.345 18.61 CHF2—CF2—NF2 369.4 1.6326 0.542 0.0085 0.0295 0.0258 1,042.93 0.00096 91.63 1.269 15.99 CF3—CF2—NF2 363.6 1.7839 0.6076 0.0068 0.02009 0.0203 1,161.13 0.00086 75.33 1.198 12.21

536.2 0.1143 0.0237 0.546 2.63334 2.3648 679.138 0.00147 684.94 2.183 62.41

461.4 0.3759 0.0968 0.0861 0.33416 0.3086 1,007.23 0.00099 301.37 1.524 32.35

456.1 0.3968 0.1006 0.0559 0.22034 0.2039 1,374.11 0.00073 208.23 1.184 22.17

458.7 0.3864 0.0986 0.0681 0.26685 0.2467 1,202.83 0.00083 246.29 1.323 26.31

475.5 0.3221 0.0796 0.1018 0.4118 0.3777 1,146.78 0.00087 315.71 1.454 32.78

478.3 0.3139 0.0783 0.1353 0.54259 0.4972 901.88 0.00111 407.39 1.819 42.48

499.2 0.2195 0.0534 0.1961 0.80611 0.7331 873.019 0.00115 423.06 1.703 43.05

478.7 0.2689 0.0667 0.0995 0.40101 0.3674 1,239.43 0.00081 257.47 1.29 26.75

481.5 0.2625 0.0657 0.1252 0.50028 0.458 1,021.68 0.00098 314.83 1.484 32.87

464.6 0.3139 0.0808 0.0842 0.32692 0.3015 1,106.62 0.0009 246.43 1.348 26.42

462 0.3219 0.0822 0.0691 0.27075 0.2499 1,277.47 0.00078 208.55 1.205 22.26

459.4 0.3302 0.0837 0.0582 0.22964 0.2122 1,428.48 0.0007 180.91 1.102 19.22

Calculation of Thermal Efficiency Equation of Thermal Efficiency

The FIG. 1 shows the principle of the ORC cycle. The efficiency may be calculated using the equation:

$\begin{matrix} {\eta = \frac{h_{3} - h_{4}}{h_{3} - h_{1}}} & (1) \end{matrix}$

Four basic equations of thermodynamics are:

dU=TdS−pdV  (2a)

dH=TdS+Vdp  (2b)

dA=−pdV−SdT  (2c)

dG=Vpd−SdT  (2d)

Also, for the ORC, the process from position 3 to position 4 is an isentropic process. Therefore,

$\begin{matrix} {{h_{3} - h_{4}} = {{PV}\mspace{14mu} \ln {\frac{P_{1}}{P_{2}}.}}} & (3) \end{matrix}$

The total heat absorption process should be from point 1 to point 3. The total heat can be calculated as

h ₃ −h ₁ =ΔH _(v) +C _(y)(T ₁ −T ₂)

the efficiency η then can be written as,

$\begin{matrix} {\eta = {\frac{h_{3} - h_{4}}{h_{3} - h_{1}} = {\frac{{PV}\mspace{14mu} \ln \frac{P_{1}}{P_{2}}}{{\Delta \; H_{v}} + {C_{p}\left( {T_{1} + T_{2}} \right)}}.}}} & (5) \end{matrix}$

The efficiency of new molecules can be estimated by the equation (5), and the useful parameters in the new molecules are calculated by the Group Contribution Method.

Systematic Error of Efficiency

A standard deviation method was used to correct the systematic error of the efficiencies calculation of the candidate molecules and give the thermal efficiency. At first, usage was made of the efficiencies

$\begin{matrix} {\eta_{a} = \frac{h_{3} - h_{4}}{h_{3} - h_{1}}} & (1) \end{matrix}$

calculated by using the enthalpy of the working fluids in software Refprop as the accurate results. Then, calculating the same efficiencies by another formula developed by using the thermodynamic data in software Refprop

$\begin{matrix} {\eta_{REFPROP} = {\frac{{PV}\mspace{14mu} \ln \frac{P_{1}}{P_{2}}}{{\Delta \; H_{v}} + {C_{p}\left( {T_{1} + T_{2}} \right)}}.}} & (2) \end{matrix}$

Comparing η_(a) and η_(REFPROP), and calculating the standard deviation σ=0.32%, one could see that the average correction to η_(REFPROP) is about 0.32%. This average error comes from the formula which is a good approximation. Then, calculations were made of the efficiencies η_(group contribution) based on the same formula as equation (2) but using the thermodynamic data estimated by the group contribution method. Comparing η_(a) and η_(group contribution) and calculating the standard deviation σ=0.65%, one could see that the average correction to η_(group contribution) is about 0.65%. The average deviation comes from both the approximate formula and the group contribution method. The results from the above mentioned calculations are listed in the following Table 2 and FIG. 2. From FIG. 2, one can see that η_(group contribution) is systematically higher than η_(a), and that the average difference is just the standard deviation. Thus, by subtracting σ=0.65% from η_(group contribution) the efficiencies of the designed molecules of working fluids are obtained. Another issue to mention is: before correction of η_(group contribution) by subtracting 0.65%, some efficiencies of the candidate working fluids are larger than 12% which are beyond the limit of the ideal Carnot cycle, which is 40/333.15=12%. Thus, after the correction, all the efficiencies are less than 12%, which is reasonable. Although the standard deviation 0.65% is calculated from the existing molecules, it is also applicable for the designed molecules.

TABLE 2 Efficiency calculations with and without group contribution. Results from known existing molecules η_(Group) σ_(Group) Substances Molecules η_(a) η_(REFPROP) σ_(REFPROP) Contribution Contribution R21 CHCl₂F 11.14% 11.71% 0.32% 12.04% 0.65% R22 CHClF₂ 11.11% 11.03% 12.28% R11 CCl₃F 11.07% 11.55% 11.92% trifluoroiodomethane CF₃I 11.05% 11.15% 11.69% R12 CCl₂F₂ 10.97% 10.85% 11.70% dimethylether CH₃OCH₃ 11.02% 11.13% 11.78% R141b FCCl₂—CH₃ 11.01% 11.47% 11.79% R152a CH₃CHF₂ 10.97% 10.96% 11.75% R123* CHCl₂CF₃ 10.87% 11.13% 11.50% R113* CCl₂FCClF₂ 10.79% 11.10% 11.50% R134a CH₂FCF₃ 10.78% 10.43% 11.40% R124* Cl—CHF—CF₃ 10.73% 10.51% 11.15% R142b ClCF₂CH₃ 10.89% 10.94% 11.22% R114 CClF₂CClF₂ 10.58% 10.48% 11.04% propyne CH≡CCH₃ 11.21% 11.45% 11.89% propylene CH₂═CHCH₃ 11.08% 10.71% 12.24% propane CH₃CH₂CH₃ 10.97% 10.57% 11.80% R245ca* CHF₂CF₂CH₂F 10.73% 10.85% 11.24% R245fa* CF₃CH₂CHF₂ 10.70% 10.77% 11.11% R236fa* CF₃CH₂CF₃ 10.48% 10.14% 10.73% R227ea* CF₃—CHF—CF₃ 10.28% 9.57% 10.47% Acetone CH₃COCH₃ 11.17% 11.90% 12.26% R236ea* CF₃—CHF—CHF₂ 10.52% 10.37% 10.91% trans-butene* CH₃CH═CHCH₃ 10.91% 11.04% 11.53% 1-butene* CH₂═CHCH₂CH₃ 10.90% 10.95% 11.37% isobutene* CH₂═C(CH₃)CH₃ 10.86% 10.87% 11.35% butane* CH₃CH₂CH₂CH₃ 10.80% 10.80% 11.21% isobutane* CH(CH₃)₃ 10.76% 10.60% 11.10% R365mfc* CF₃—CF₂—CH₂—CF₃ 10.58% 10.71% 10.75% perfluorobutane* CF₃—CF₂—CF₂—CF₃ 9.67% 9.02% 9.80% cis-butene CH₃CH═CHCH₃ 10.96% 11.20% 11.53%

TABLE 3 Results from efficiency calculations using group contribution method and final efficiency after calculations using enthalpies, software Refprop and group contribution method. Results from molecules according to the present invention P1 P2 Molecules MPa MPa η _(GC) η CH3—NHF 0.7866 0.2323 12.15% 11.50% CH2F—NHF 0.8415 0.2437 11.97% 11.32% CHF2—NHF 0.8863 0.2567 11.80% 11.15% CF3—NHF 0.9737 0.2914 11.60% 10.95% CH3—NF2 1.1723 0.3875 11.89% 11.23% CH2F—NF2 2.698 0.9858 12.10% 11.45% CHF2—NF2 2.859 1.0426 12.07% 11.42% CF3—NF2 3.1125 1.1585 12.14% 11.49% CH3—CH2—NHF 0.3772 0.0957 11.91% 11.26% CH2F—CH2—NHF 0.398 0.0984 11.78% 11.12% CHF2—CH2—NHF 0.418 0.1032 11.63% 10.98% CF3—CH2—NHF 0.4641 0.119 11.42% 10.77% CH3—CHF—NHF 0.396 0.1002 11.76% 11.11% CH2F—CHF—NHF 0.418 0.1032 11.63% 10.98% CHF2—CHF—NHF 0.4393 0.1083 11.48% 10.83% CF3—CHF—NHF 0.4879 0.1249 11.28% 10.63% CH3—CF2—NHF 0.4388 0.1152 11.56% 10.91% CH2F—CF2—NHF 0.4641 0.119 11.42% 10.77% CHF2—CF2—NHF 0.4879 0.1249 11.28% 10.63% CF3—CF2—NHF 0.5407 0.1435 11.08% 10.43% CH3—CH2—NF2 1.2373 0.4077 11.38% 10.73% CH2F—CH2—NF2 1.3348 0.4322 11.24% 10.59% CHF2—CH2—NF2 1.411 0.4565 11.09% 10.44% CF3—CH2—NF2 1.5417 0.5128 10.92% 10.27% CH3—CHF—NF2 1.3039 0.4297 11.23% 10.57% CH2F—CHF—NF2 1.411 0.4565 11.09% 10.44% CHF2—CHF—NF2 1.4895 0.4817 10.96% 10.31% CF3—CHF—NF2 1.6326 0.542 10.80% 10.15% CH3—CF2—NF2 1.4215 0.4817 11.03% 10.38% CH2F—CF2—NF2 1.5417 0.5128 10.92% 10.27% CHF2—CF2—NF2 1.6326 0.542 10.80% 10.15% CF3—CF2—NF2 1.7839 0.6076 10.67% 10.02%

0.1143 0.0237 12.57% 11.92%

0.3759 0.0968 12.11% 11.46%

0.3968 0.1006 11.90% 11.25%

0.3864 0.0986 12.01% 11.36%

0.3221 0.0796 12.26% 11.61%

0.3139 0.0783 12.29% 11.64%

0.2195 0.0534 12.39% 11.74%

0.2689 0.0667 12.07% 11.42%

0.2625 0.0657 12.17% 11.52%

0.3139 0.0808 11.94% 11.29%

0.3219 0.0822 11.83% 11.18%

0.3302 0.0837 11.72% 11.07% Note: ηGC is calculated by the Group Contribution Method η is the final estimated efficiency η is equal to: (η _(GC)) − (systematic error) The systematic error is shown above and is the standard deviation σ = 0.65%

Calculation of Flammability and Toxicity Prediction of Flammability of Gases by Using the F-Number Analysis

F=1−(L/U)^(0.5)

L is the lower flammability limit U is the upper flammability limit F=0.0-0.2 vaguely flammable F=0.2-0.4 weakly flammable F=0.4-0.6 normally flammable F=0.6-0.8 strongly flammable F=0.8-1.0 super flammable F=p1(1+p2C1+p3ROE+p4RCO+p5RCOO+p6RNH+p7RRNG+p8RARM+p9RUS)×(1+p10RF+p11RCI+p12RBr+p13ROH+p14RNO2+p15RNH2+p16RCN+P17RCOOH)

TABLE 4 Parameter values obtained by the analysis No. Description Obtained value p1 Main coefficient 0.581 p2 If one carbon −0.194 p3 Ether 0.134 p4 Carbonyl 0.028 p5 Ester −0.097 p6 NH −0.014 p7 Aliphatic ring 0.299 p8 Aromatic ring −0.125 p9 Unsaturation 0.290 p10 F −0.344 p11 Cl −0.985 p12 Br −3.160 p13 OH 0.284 p14 NO2 0.527 p15 NH2 −0.344 p16 CN −0.566 p17 COOH −0.850

C1 takes the value of 1 or 0 according to whether the molecule is a compound of mono-carbon skeleton or not. However, the methane derivatives that contain CO, COO, CN, or COOH group are treated exceptionally; C1 takes the value of 0 for these compounds. ROE, RCO, RCOO, and RNH denote numbers of ether, carbonyl, ester, and imine groups, respectively, divided by the total number of skeletal carbons. RRNG and RARM denote numbers of aliphatic and aromatic rings, respectively, divided by the total number of skeletal carbons. RUS denotes the total number of unsaturation in the carbon skeleton including aliphatic and aromatic rings divided by the total number of skeletal carbons. RF, RCI, and so on, and RCOOH denote numbers of F, Cl, and so on, and COOH, respectively, divided by the total number of hydrogen atoms in the corresponding pure hydrocarbon molecule.

Reference of Flammability:

R600 F=0.581 R134a F=0.4478 Application of Group Contribution Method for Predicting the Toxicity of Organic Chemicals

Set C=−log(LC50)=ΣNiai

Equation: LC50=concentration casing 50% mortality in fathead minnow

Ni=number of group of type i

ai=contribution of group of type i

Currently, the C of common refrigerants is less than 2. Therefore, the working fluids with C values less than 2 are recommended.

TABLE 5 Toxicity contribution for substituent groups in the data-set chemicals for fathead minnow toxicity No. Group Name Contribution values 1 CH3 0.6791 2 CH2 0.2925 3 CH 0.3305 4 C 0.06214 5 F 0.4034 6 Cl 0.8712 7 Br 0.8515 8 O −0.4086 9 OH 0.3392 10 CO −0.2842 11 CHO 1.331 12 ArCH 0.4575 13 ArC 0.2913 14 CN 0.6333 15 N −0.7043 16 NH −0.1157 17 NH2 0.1883 18 NO2 0.7276 For example:

TABLE 4 Flammability and toxicity calculations made by group contribution calculations. Results from molecules according to the present invention Flammability Toxicity Molecules (F) C CH3—NHF 0.420579 0.9668 CH2F—NHF 0.381006 0.9836 CHF2—NHF 0.341433 1.425 CF3—NHF 0.30186 1.56004 CH3—NF2 0.387741 0.7816 CH2F—NF2 0.347468 0.7984 CHF2—NF2 0.307196 1.2398 CF3—NF2 0.266923 1.37484 CH3—CH2—NHF 0.543856 1.2593 CH2F—CH2—NHF 0.510778 1.2761 CHF2—CH2—NHF 0.477701 1.7175 CF3—CH2—NHF 0.444623 1.2593 CH3—CHF—NHF 0.510778 1.7007 CH2F—CHF—NHF 0.477701 1.7175 CHF2—CHF—NHF 0.444623 2.1589 CF3—CHF—NHF 0.411546 2.29394 CH3—CF2—NHF 0.477701 1.83574 CH2F—CF2—NHF 0.444623 1.85254 CHF2—CF2—NHF 0.411546 2.29394 CF3—CF2—NHF 0.378468 2.42898 CH3—CH2—NF2 0.514379 1.0741 CH2F—CH2—NF2 0.481068 1.0909 CHF2—CH2—NF2 0.447757 1.5323 CF3—CH2—NF2 0.414447 1.66734 CH3—CHF—NF2 0.481068 1.5155 CH2F—CHF—NF2 0.447757 1.5323 CHF2—CHF—NF2 0.414447 1.9737 CF3—CHF—NF2 0.381136 2.10874 CH3—CF2—NF2 0.447757 1.65054 CH2F—CF2—NF2 0.414447 1.66734 CHF2—CF2—NF2 0.381136 2.10874 CF3—CF2—NF2 0.347825 2.24378

0.748038 0.4693

0.619375 1.3521

0.490713 1.62218

0.555044 1.48714

0.619375 1.04574

0.683706 0.9107

0.687424 0.2841

0.558062 0.86054

0.622743 0.7255

0.558062 1.1669

0.493381 1.30194

0.4287 1.43698

Calculation of Ozone Depletion Potential

No bromine or chlorine in the molecules. Thus, ODP is 0. 

1. An organic Rankine cycle working fluid comprising at least one compound having a structure according to Formula (I): RNQ wherein R is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl, N is the element nitrogen, the connection of R—N is a ring structure or a straight chain structure, and Q is chosen from a hydrogen atom and/or at least one fluorine atom.
 2. An organic Rankine cycle working fluid according to claim 1, said at least one compound is either of the Formula (II): R¹NH_(n)F_(2-n). wherein R¹ is fluorinated or non-fluorinated methyl, ethyl, vinyl, or ethynyl, and n is 0 or 1; or the Formula (III):

wherein R² and R³ are independently chosen from H₂, F₂ and HF, and p is 0 or
 1. 3. A working fluid according to claim 2, wherein R¹ in Formula (II) is a fluorinated or non-fluorinated methyl or ethyl group.
 4. A working fluid according to claim 3, wherein said compound is chosen from CH₃NHF, CH₂FNHF, CHF₂NHF, CF₃NHF, CH₃NF₂, CH₂FNF₂, CHF₂NF₂, CF₃NF₂, C₂H₅NHF, CH₂FCH₂NHF, CHF₂CH₂NHF, CH₃CHFNHF, CH₂FCHFNHF, C₂H₅NF₂, CH₂FCH₂NF₂, CH₃CHFNF₂, and CHF₂CF₂NF₂.
 5. A working fluid according to claim 4, wherein said compound is chosen from CH₃NF₂, CH₂FNF₂, CHF₂NF₂, and CF₃NF₂.
 6. A working fluid according to claim 2, wherein p in Formula (II) is
 1. 7. A working fluid according to claim 6, wherein R² in Formula (II) contains at least one fluorine.
 8. A working fluid according to claim 7, wherein said compound is tetrafluoroaziridine.
 9. A process for converting thermal energy to mechanical energy in an organic Rankine cycle comprising the steps of: a) vaporizing a liquid working fluid according to claim 1, by bringing it in contact with a heat source; b) expanding the vaporized working fluid, wherein said heat is converted into mechanical work; and c) cooling the expanded vaporized working fluid with a cooling source to condense the vapor to liquid phase.
 10. A process according to claim 9, wherein the temperature of the work fluid after being brought in contact with a heat source in a) is at most 100° C.
 11. A process according to claim 10, wherein said temperature is 25° C. to 90° C.
 12. An organic Rankine cycle system using the working fluid according to claim 1 for a heat cycle.
 13. An organic Rankine cycle system comprising: (a) a working fluid according to claim 1; (b) a heat exchanging device containing said working fluid, connected to a heat source, for vaporizing the working fluid and producing vaporized working fluid; (c) an expansion device responsive to said vaporized working fluid for expanding said working fluid vapor resulting in heat depleted working fluid; (d) an electric generator driven by said expansion device for producing electrical power; (e) a condenser for condensing the heat depleted working fluid and producing condensate; and (f) means for effecting the return of said condensate to said heat exchanging device.
 14. An organic Rankine cycle system according to claim 13, wherein the heat source is chosen from heat from a boiler or a fuel cell, waste heat from an industrial or farming process, geothermal heat, waste heat from a combustion engine or power plant, or solar heat.
 15. An organic Rankine cycle system according to claim 13, wherein the expander is a turbine, screw expander, scroll expander, or piston expander.
 16. (canceled)
 17. (canceled)
 18. A method for power generation comprising transfer of heat using a working fluid according to claim
 1. 19. A method for power generation according to claim 1, using a Rankine cycle or a modification thereof to generate work from heat.
 20. A compound having the Formula (IV): 